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sorry to add to this mayhem but I am also suffering from the same problem. I've read through the other posts but I can't make sense of most of the detailed ones. I have 5 variables 4 of which are I(2) and one which is I(0). Firstly can I still use the johansen test or is that only for I(1) and I(0) ...

having the exact same problem right now, 4 of my variables are I(2) and one is I(0). My supervisor is absolutely useless she said that I could still run a johansen test and it was fine but I have just discovered that is not the case. Did you find a solution to the issue? I would really really apprec...